Quantum chemistry provides key applications for near-term quantum computing, but these are greatly complicated by the presence of noise. In this work we present an efficient ansatz for the computation of two-electron atoms and molecules within a hybrid quantum-classical algorithm. The ansatz exploits the fundamental structure of the two-electron system, and treating the nonlocal and local degrees of freedom on the quantum and classical computers, respectively. Here the nonlocal degrees of

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... m scale linearly with respect to basis-set size, giving a linear ansatz with only O(1) circuit preparations required for reduced state tomography. We implement this benchmark with error mitigation on two publicly available quantum computers, calculating accurate dissociation curves for 4- and 6- qubit calculations of H_2^ and H_3^+.